In this article we established the concept of multi-continuity in minimal structure spaces (in short $\mathscr{M}$ space) and notion product space multiset topological space. Continuity between $\mathscr{M}$-space, generalized topology ideal spaces. We have investigated some basic properties $\mathscr{M}$–continuity space, such as composition $\mathscr{M}$–continuous functions, functions etc.

Gamma is a kernel language in which programs are described in terms of multiset transformations following the chemical reaction metaphor. Previous work has demonstrated its signiicance for the construction of massively parallel programs but also highlighted some limitations. We introduce a higher-order extension of this formalism unifying the program and data syntactic categories. As a conseque...

This Isabelle/HOL formalization introduces a nested multiset datatype and de nes Dershowitz and Manna's nested multiset order. The order is proved well founded and linear. By removing one constructor, we transform the nested multisets into hereditary multisets. These are isomorphic to the syntactic ordinals the ordinals can be recursively expressed in Cantor normal form. Addition, subtraction, ...

We compare the expressive power of a class of well-structured transition systems that includes relational automata, Petri nets, lossy channel systems, and constrained multiset rewriting systems. For each one of these models we study the class of languages generated by labelled transition systems describing their semantics. We consider here two types of accepting conditions: coverability and rea...

We investigate model checking of a computation model called Constrained Multiset Rewriting Systems (CMRS). A CMRS operates on configurations which are multisets of monadic predicate symbols, each with an argument ranging over the natural numbers. The transition relation is defined by a finite set of rewriting rules which are conditioned by simple inequalities on variables and constants. This mo...